Hot chocolate effect
Encyclopedia
The Hot Chocolate Effect is a phenomenon of wave mechanics
first documented in 1982 by Frank Crawford, where the pitch heard from tapping a cup of hot liquid rises after the addition of a soluble powder. It typically arises in the making of hot chocolate
or instant coffee
, but also occurs in other situations such as adding salt to supersaturated
hot water or cold beer.
It can be observed by pouring hot milk into a mug, stirring in chocolate powder, and tapping the bottom of the mug with a spoon while the milk is still in motion. The pitch of the taps will increase progressively with no relation to the speed or force of tapping. Subsequent stirring will gradually decrease the pitch again.
The phenomenon is explained by the effect of bubble density on the speed of sound
in the liquid. The note heard is the frequency
of a standing wave
where a quarter wavelength
is the distance between the base of the mug and the liquid surface.
This frequency f is equal to the speed
v of the wave
divided
by four times the height of the water column h:
Upon initial stirring, entrained gas bubbles reduce the speed of sound in the liquid, lowering the frequency. As the bubbles clear, sound travels faster in the liquid and the frequency increases.
Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...
first documented in 1982 by Frank Crawford, where the pitch heard from tapping a cup of hot liquid rises after the addition of a soluble powder. It typically arises in the making of hot chocolate
Hot chocolate
Hot chocolate is a heated beverage typically consisting of shaved chocolate, melted chocolate or cocoa powder, heated milk or water, and sugar...
or instant coffee
Instant coffee
Instant coffee, also called soluble coffee and coffee powder, is a beverage derived from brewed coffee beans. Instant coffee is commercially prepared by either freeze-drying or spray drying, after which it can be rehydrated...
, but also occurs in other situations such as adding salt to supersaturated
Supersaturation
The term supersaturation refers to a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances...
hot water or cold beer.
It can be observed by pouring hot milk into a mug, stirring in chocolate powder, and tapping the bottom of the mug with a spoon while the milk is still in motion. The pitch of the taps will increase progressively with no relation to the speed or force of tapping. Subsequent stirring will gradually decrease the pitch again.
The phenomenon is explained by the effect of bubble density on the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
in the liquid. The note heard is the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
of a standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
where a quarter wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
is the distance between the base of the mug and the liquid surface.
This frequency f is equal to the speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
v of the wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
divided
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
by four times the height of the water column h:
Upon initial stirring, entrained gas bubbles reduce the speed of sound in the liquid, lowering the frequency. As the bubbles clear, sound travels faster in the liquid and the frequency increases.